{"work":{"id":"83078d0b-6c02-4fc5-822d-4da4204fd057","openalex_id":"https://openalex.org/W2901859177","doi":"10.48550/arxiv.1811.04968","arxiv_id":"1811.04968","raw_key":null,"title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations","authors":null,"authors_text":"Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith","year":2018,"venue":"quant-ph","abstract":"PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.","external_url":"https://arxiv.org/abs/1811.04968","cited_by_count":233,"metadata_source":"pith","metadata_fetched_at":"2026-08-05T02:28:24.338817+00:00","pith_arxiv_id":"1811.04968","created_at":"2026-05-09T06:14:30.705567+00:00","updated_at":"2026-08-05T02:28:24.338817+00:00","title_quality_ok":true,"display_title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations","render_title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations"},"hub":{"state":{"work_id":"83078d0b-6c02-4fc5-822d-4da4204fd057","tier":"super_hub","tier_reason":"100+ Pith inbound or 10,000+ external citations","pith_inbound_count":160,"external_cited_by_count":233,"distinct_field_count":14,"first_pith_cited_at":"2024-03-05T14:07:37+00:00","last_pith_cited_at":"2026-07-09T10:53:02+00:00","author_build_status":"needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-08-22T02:19:18.807782+00:00","tier_text":"super_hub"},"tier":"super_hub","role_counts":[{"context_role":"background","n":16},{"context_role":"method","n":10}],"polarity_counts":[{"context_polarity":"background","n":16},{"context_polarity":"use_method","n":10}],"runs":{"ask_index":{"job_type":"ask_index","status":"succeeded","result":{"title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations","claims":[{"claim_text":"PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework co","claim_type":"abstract","evidence_strength":"source_metadata"},{"claim_text":"hex topology, only allow two-qubit gates between physically adjacent qubits. Consequently, synthesized quantum circuits must be transpiled to respect these connectivity constraints, a process that typically introduces additional two-qubit gates and increases the overall circuit depth. Existing quantum circuit transpilers, such as those provided by Qiskit [26], TKET [30], and Pennylane [5], offer general- purpose transpilation routines that route arbitrary quantum circuits to a target architectur","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"passive steering-based state preparation as a defense against adversarial attacks. We first outline the experimental setup. Next, we identify suitable parameters for controlled passive steering. Finally, we present the results for both hybrid and fully quantum QML models. A. Experimental Setup We conducted our experiments using the PennyLane v0.44.0 [29] simulator framework with Python v3.11.3 and PyTorch v2.9.1 [30]. The proposed defense mechanism was evaluated using three different QML models,","claim_type":"method","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"signature of the barren plateau phenomenon extended to non-variational settings [5, 26]. This formally con- firms that for high-dimensional latents embedded via deep scrambling circuits, the concentration of measure is excep- tionally severe. To verify this analytical scaling, we performed ex- act state-vector simulations for 𝑛∈ [ 3, 8] qubits using PennyLane [2]. By sampling 500 independent circuit re- alisations per system size, we observed that the log-log regression of the variance against𝑑 ","claim_type":"method","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"the upper bound is updated to the middle point, and effective mutants are selected (lines 16-17). Otherwise, the lower bound is set to a larger value (line 19). The search process terminates when the search bounds can no longer be refined (line 20). Finally, we can obtain a set of effective mutants that cover different configurations of gate percentage. 4 Evaluation We implement QuanForge using PennyLane 0.42 [7] and Pytorch 2.8 [45]. All experiments are conducted on systems equipped with Intel ","claim_type":"method","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"reference architecture also outlines future phases with more tightly integrated execution models, including near-time coupling and support for outer decoders. 8 5.3 Stack 3: IonQ IonQ provides access to trapped-ionQPU resources through itsQuantum Platform[37, 49], which spans scheduling, compilation, tenant management, and observability. It integrates with Qiskit [59], CUDA-Q [26], and PennyLane [57] SDKs. The primary deployment model is cloud-managed; on-premises and federated access pathways a","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"ics [11], fluid dynamics [12], and quantum chemistry [13, 14, 15, 16]. We can only list a limited number of examples here; the broader literature is vast. This scientific breadth has driven grow- ing demand for software tools that support the construction and analysis of block encodings. General-purpose frameworks includeQiskit[ 17],Cirq[ 18],PennyLane[ 19],Qrisp[ 20], and Date: May 11, 2026. The work of M. Deiml and D. Peterseim is partially funded by the Deutsche Forschungsgemeinschaft (DFG, G","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"}],"why_cited":"Pith tracks PennyLane: Automatic differentiation of hybrid quantum-classical computations because it crossed a citation-hub threshold. Current citing contexts most often use it as background evidence (16 contexts).","role_counts":[{"n":16,"context_role":"background"},{"n":9,"context_role":"method"}]},"error":null,"updated_at":"2026-05-20T14:11:58.697925+00:00"},"author_expand":{"job_type":"author_expand","status":"succeeded","result":{"authors_linked":[{"id":"054f30d4-bb78-40fb-898e-8e17b0e29a78","orcid":null,"display_name":"Ville Bergholm"},{"id":"936108d4-1ada-4cc3-9929-d30de16b5752","orcid":null,"display_name":"Josh Izaac"},{"id":"18d03a18-3d7a-42d7-b787-fa302475e397","orcid":null,"display_name":"Maria Schuld"},{"id":"20df2e19-f54f-4552-b254-0d2900e27b32","orcid":null,"display_name":"Christian Gogolin"},{"id":"c2108f5d-3846-4d09-aa77-4937ac2d0a16","orcid":null,"display_name":"Shahnawaz Ahmed"},{"id":"f95cb9a6-df43-4205-965f-15e6cae28087","orcid":null,"display_name":"Vishnu Ajith"}]},"error":null,"updated_at":"2026-05-20T14:11:58.694272+00:00"},"context_extract":{"job_type":"context_extract","status":"succeeded","result":{"enqueued_papers":25},"error":null,"updated_at":"2026-05-14T08:18:20.927217+00:00"},"graph_features":{"job_type":"graph_features","status":"succeeded","result":{"co_cited":[{"title":"Adam: A Method for Stochastic Optimization","work_id":"1910796d-9b52-4683-bf5c-de9632c1028b","shared_citers":15},{"title":"A Quantum Approximate Optimization Algorithm","work_id":"5a33d9f3-407a-4c7e-a119-ff581c66b173","shared_citers":12},{"title":"Quantum computing with Qiskit","work_id":"5dd3e61a-2250-4afb-a3d4-dd7202477631","shared_citers":9},{"title":"Classification with quantum neural networks on near term processors","work_id":"f3ac8797-5c26-456c-827e-e8a239183dfa","shared_citers":5},{"title":"Explaining and Harnessing Adversarial Examples","work_id":"2cedf8f6-7539-4c49-8136-f42a20487146","shared_citers":5},{"title":"Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms","work_id":"6714d44f-1b5e-4141-9450-ea09a7e724b0","shared_citers":5},{"title":"Towards Deep Learning Models Resistant to Adversarial Attacks","work_id":"b20a57fa-4b7d-40ec-8b6a-ce48234630de","shared_citers":5},{"title":"Expressibility and entangling capability of parameter- ized quantum circuits for hybrid quantum-classical al- gorithms","work_id":"406c5dfe-2cbc-48d9-ac6d-9387d839a353","shared_citers":4},{"title":"Qrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantum Computers","work_id":"42a4e981-0ad5-4428-ac29-9dc691ae58d1","shared_citers":4},{"title":"115.205901","work_id":"4deaf489-c81b-4322-bb0a-41188b0ad4db","shared_citers":3},{"title":"Arute et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019), doi:10.1038/s41586-019-1666-5","work_id":"39c8860f-db19-43fe-98b6-a367aaa5b3d8","shared_citers":3},{"title":"Better than classical? the subtle art of benchmark- ing quantum machine learning models","work_id":"a1f893c3-b0a0-42bf-9b3a-bfafa76ca8a8","shared_citers":3},{"title":"Exponential quantum advantage in processing massive classical data","work_id":"b4d46a22-0129-43ee-924b-421290b5b759","shared_citers":3},{"title":"https://doi.org/10.1038/ncomms5213","work_id":"39da8f39-782e-47a1-bb98-e482b344cb2a","shared_citers":3},{"title":"Jones and J","work_id":"e0b271ac-a990-4515-9e49-4de034e88acc","shared_citers":3},{"title":"McClean, Sergio Boixo, Vadim N","work_id":"80a01651-ca79-4838-8a0a-f2c1d51bcc27","shared_citers":3},{"title":"Q#: Enabling Scalable Quantum Computing and Development with a High-level DSL","work_id":"abb288e4-c48d-415f-967f-8646701c441f","shared_citers":3},{"title":"Qiskit: An Open-source Framework for Quantum Computing , year =","work_id":"ebd0aee5-4e27-4b45-b6dc-e7ab9b6f91c1","shared_citers":3},{"title":"Quantum-Enhanced Convergence of Physics-Informed Neural Networks","work_id":"37e8fc32-3aee-4620-97e4-51c254fdde0b","shared_citers":3},{"title":"Quantum measurements and the Abelian Stabilizer Problem","work_id":"0840a06c-bc13-4619-9fd6-9abb6810e838","shared_citers":3},{"title":"2019 , month = sep, volume =","work_id":"2dd6b155-5b3c-496e-b65e-19419459eaee","shared_citers":2},{"title":"AQ-PINNs: Attention-enhanced quantum physics-informed neural networks for carbon-efficient climate modeling","work_id":"74945939-64f4-4a58-81d9-9292d18d32d3","shared_citers":2},{"title":"arXiv:2003.02831 , year =","work_id":"a215edcc-2a86-4b7d-a31c-fde1a2aea78b","shared_citers":2},{"title":"arXiv preprint arXiv:2109.11676 , year =","work_id":"8e586ab7-ddab-46b1-8418-fcd98fbb5c47","shared_citers":2}],"time_series":[{"n":1,"year":2024},{"n":1,"year":2025},{"n":69,"year":2026}],"dependency_candidates":[]},"error":null,"updated_at":"2026-05-14T08:28:04.674255+00:00"},"identity_refresh":{"job_type":"identity_refresh","status":"succeeded","result":{"items":[{"title":"Qwen3 Technical Report","outcome":"unchanged","work_id":"25a4e30c-1232-48e7-9925-02fa12ba7c9e","resolver":"local_arxiv","confidence":0.98,"old_work_id":"25a4e30c-1232-48e7-9925-02fa12ba7c9e"}],"counts":{"fixed":0,"merged":0,"unchanged":1,"quarantined":0,"needs_external_resolution":0},"errors":[],"attempted":1},"error":null,"updated_at":"2026-05-14T08:18:04.934887+00:00"},"role_polarity":{"job_type":"role_polarity","status":"succeeded","result":{"title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations","claims":[{"claim_text":"PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework co","claim_type":"abstract","evidence_strength":"source_metadata"},{"claim_text":"hex topology, only allow two-qubit gates between physically adjacent qubits. Consequently, synthesized quantum circuits must be transpiled to respect these connectivity constraints, a process that typically introduces additional two-qubit gates and increases the overall circuit depth. Existing quantum circuit transpilers, such as those provided by Qiskit [26], TKET [30], and Pennylane [5], offer general- purpose transpilation routines that route arbitrary quantum circuits to a target architectur","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"passive steering-based state preparation as a defense against adversarial attacks. We first outline the experimental setup. Next, we identify suitable parameters for controlled passive steering. Finally, we present the results for both hybrid and fully quantum QML models. A. Experimental Setup We conducted our experiments using the PennyLane v0.44.0 [29] simulator framework with Python v3.11.3 and PyTorch v2.9.1 [30]. The proposed defense mechanism was evaluated using three different QML models,","claim_type":"method","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"signature of the barren plateau phenomenon extended to non-variational settings [5, 26]. This formally con- firms that for high-dimensional latents embedded via deep scrambling circuits, the concentration of measure is excep- tionally severe. To verify this analytical scaling, we performed ex- act state-vector simulations for 𝑛∈ [ 3, 8] qubits using PennyLane [2]. By sampling 500 independent circuit re- alisations per system size, we observed that the log-log regression of the variance against𝑑 ","claim_type":"method","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"the upper bound is updated to the middle point, and effective mutants are selected (lines 16-17). Otherwise, the lower bound is set to a larger value (line 19). The search process terminates when the search bounds can no longer be refined (line 20). Finally, we can obtain a set of effective mutants that cover different configurations of gate percentage. 4 Evaluation We implement QuanForge using PennyLane 0.42 [7] and Pytorch 2.8 [45]. All experiments are conducted on systems equipped with Intel ","claim_type":"method","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"reference architecture also outlines future phases with more tightly integrated execution models, including near-time coupling and support for outer decoders. 8 5.3 Stack 3: IonQ IonQ provides access to trapped-ionQPU resources through itsQuantum Platform[37, 49], which spans scheduling, compilation, tenant management, and observability. It integrates with Qiskit [59], CUDA-Q [26], and PennyLane [57] SDKs. The primary deployment model is cloud-managed; on-premises and federated access pathways a","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"ics [11], fluid dynamics [12], and quantum chemistry [13, 14, 15, 16]. We can only list a limited number of examples here; the broader literature is vast. This scientific breadth has driven grow- ing demand for software tools that support the construction and analysis of block encodings. General-purpose frameworks includeQiskit[ 17],Cirq[ 18],PennyLane[ 19],Qrisp[ 20], and Date: May 11, 2026. The work of M. Deiml and D. Peterseim is partially funded by the Deutsche Forschungsgemeinschaft (DFG, G","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"}],"why_cited":"Pith tracks PennyLane: Automatic differentiation of hybrid quantum-classical computations because it crossed a citation-hub threshold. Current citing contexts most often use it as background evidence (16 contexts).","role_counts":[{"n":16,"context_role":"background"},{"n":9,"context_role":"method"}]},"error":null,"updated_at":"2026-05-20T14:11:58.700222+00:00"},"summary_claims":{"job_type":"summary_claims","status":"succeeded","result":{"title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations","claims":[{"claim_text":"PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework co","claim_type":"abstract","evidence_strength":"source_metadata"}],"why_cited":"Pith tracks PennyLane: Automatic differentiation of hybrid quantum-classical computations because it crossed a citation-hub threshold.","role_counts":[]},"error":null,"updated_at":"2026-05-14T08:27:56.000876+00:00"}},"summary":{"title":"PennyLane: Automatic differentiation of hybrid quantum-classical computations","claims":[{"claim_text":"PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework co","claim_type":"abstract","evidence_strength":"source_metadata"}],"why_cited":"Pith tracks PennyLane: Automatic differentiation of hybrid quantum-classical computations because it crossed a citation-hub threshold.","role_counts":[]},"graph":{"co_cited":[{"title":"Adam: A Method for Stochastic Optimization","work_id":"1910796d-9b52-4683-bf5c-de9632c1028b","shared_citers":15},{"title":"A Quantum Approximate Optimization Algorithm","work_id":"5a33d9f3-407a-4c7e-a119-ff581c66b173","shared_citers":12},{"title":"Quantum computing with Qiskit","work_id":"5dd3e61a-2250-4afb-a3d4-dd7202477631","shared_citers":9},{"title":"Classification with quantum neural networks on near term processors","work_id":"f3ac8797-5c26-456c-827e-e8a239183dfa","shared_citers":5},{"title":"Explaining and Harnessing Adversarial Examples","work_id":"2cedf8f6-7539-4c49-8136-f42a20487146","shared_citers":5},{"title":"Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms","work_id":"6714d44f-1b5e-4141-9450-ea09a7e724b0","shared_citers":5},{"title":"Towards Deep Learning Models Resistant to Adversarial Attacks","work_id":"b20a57fa-4b7d-40ec-8b6a-ce48234630de","shared_citers":5},{"title":"Expressibility and entangling capability of parameter- ized quantum circuits for hybrid quantum-classical al- gorithms","work_id":"406c5dfe-2cbc-48d9-ac6d-9387d839a353","shared_citers":4},{"title":"Qrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantum Computers","work_id":"42a4e981-0ad5-4428-ac29-9dc691ae58d1","shared_citers":4},{"title":"115.205901","work_id":"4deaf489-c81b-4322-bb0a-41188b0ad4db","shared_citers":3},{"title":"Arute et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019), doi:10.1038/s41586-019-1666-5","work_id":"39c8860f-db19-43fe-98b6-a367aaa5b3d8","shared_citers":3},{"title":"Better than classical? the subtle art of benchmark- ing quantum machine learning models","work_id":"a1f893c3-b0a0-42bf-9b3a-bfafa76ca8a8","shared_citers":3},{"title":"Exponential quantum advantage in processing massive classical data","work_id":"b4d46a22-0129-43ee-924b-421290b5b759","shared_citers":3},{"title":"https://doi.org/10.1038/ncomms5213","work_id":"39da8f39-782e-47a1-bb98-e482b344cb2a","shared_citers":3},{"title":"Jones and J","work_id":"e0b271ac-a990-4515-9e49-4de034e88acc","shared_citers":3},{"title":"McClean, Sergio Boixo, Vadim N","work_id":"80a01651-ca79-4838-8a0a-f2c1d51bcc27","shared_citers":3},{"title":"Q#: Enabling Scalable Quantum Computing and Development with a High-level DSL","work_id":"abb288e4-c48d-415f-967f-8646701c441f","shared_citers":3},{"title":"Qiskit: An Open-source Framework for Quantum Computing , year =","work_id":"ebd0aee5-4e27-4b45-b6dc-e7ab9b6f91c1","shared_citers":3},{"title":"Quantum-Enhanced Convergence of Physics-Informed Neural Networks","work_id":"37e8fc32-3aee-4620-97e4-51c254fdde0b","shared_citers":3},{"title":"Quantum measurements and the Abelian Stabilizer Problem","work_id":"0840a06c-bc13-4619-9fd6-9abb6810e838","shared_citers":3},{"title":"2019 , month = sep, volume =","work_id":"2dd6b155-5b3c-496e-b65e-19419459eaee","shared_citers":2},{"title":"AQ-PINNs: Attention-enhanced quantum physics-informed neural networks for carbon-efficient climate modeling","work_id":"74945939-64f4-4a58-81d9-9292d18d32d3","shared_citers":2},{"title":"arXiv:2003.02831 , year =","work_id":"a215edcc-2a86-4b7d-a31c-fde1a2aea78b","shared_citers":2},{"title":"arXiv preprint arXiv:2109.11676 , year =","work_id":"8e586ab7-ddab-46b1-8418-fcd98fbb5c47","shared_citers":2}],"time_series":[{"n":1,"year":2024},{"n":1,"year":2025},{"n":69,"year":2026}],"dependency_candidates":[]},"authors":[{"id":"20df2e19-f54f-4552-b254-0d2900e27b32","orcid":null,"display_name":"Christian Gogolin","source":"manual","import_confidence":0.72},{"id":"936108d4-1ada-4cc3-9929-d30de16b5752","orcid":null,"display_name":"Josh Izaac","source":"manual","import_confidence":0.72},{"id":"18d03a18-3d7a-42d7-b787-fa302475e397","orcid":null,"display_name":"Maria Schuld","source":"manual","import_confidence":0.72},{"id":"c2108f5d-3846-4d09-aa77-4937ac2d0a16","orcid":null,"display_name":"Shahnawaz Ahmed","source":"manual","import_confidence":0.72},{"id":"054f30d4-bb78-40fb-898e-8e17b0e29a78","orcid":null,"display_name":"Ville Bergholm","source":"manual","import_confidence":0.72},{"id":"f95cb9a6-df43-4205-965f-15e6cae28087","orcid":null,"display_name":"Vishnu Ajith","source":"manual","import_confidence":0.72}]}}